Delft University of Technology
Numerical Investigation into the Effect of Splats and Pores on the Thermal Fracture of AirPlasma-Sprayed Thermal Barrier Coatings
Krishnasamy, Jayaprakash; Ponnusami, Sathiskumar A.; Turteltaub, Sergio; van der Zwaag, Sybrand
DOI10.1007/s11666-019-00949-yPublication date2019Document VersionFinal published versionPublished inJournal of Thermal Spray Technology
Citation (APA)Krishnasamy, J., Ponnusami, S. A., Turteltaub, S., & van der Zwaag, S. (2019). Numerical Investigation intothe Effect of Splats and Pores on the Thermal Fracture of Air Plasma-Sprayed Thermal Barrier Coatings.Journal of Thermal Spray Technology, 28(8), 1881-1892. https://doi.org/10.1007/s11666-019-00949-y
Important noteTo cite this publication, please use the final published version (if applicable).Please check the document version above.
CopyrightOther than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consentof the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Takedown policyPlease contact us and provide details if you believe this document breaches copyrights.We will remove access to the work immediately and investigate your claim.
This work is downloaded from Delft University of Technology.For technical reasons the number of authors shown on this cover page is limited to a maximum of 10.
https://doi.org/10.1007/s11666-019-00949-yhttps://doi.org/10.1007/s11666-019-00949-y
PEER REVIEWED
Numerical Investigation into the Effect of Splats and Poreson the Thermal Fracture of Air Plasma-Sprayed Thermal BarrierCoatings
Jayaprakash Krishnasamy1 • Sathiskumar A. Ponnusami2 • Sergio Turteltaub1 •
Sybrand van der Zwaag1
Submitted: 1 July 2019 / in revised form: 24 October 2019
� The Author(s) 2019
Abstract The effect of splat interfaces on the fracture
behavior of air plasma-sprayed thermal barrier coatings
(APS-TBC) is analyzed using finite element modeling
involving cohesive elements. A multiscale approach is
adopted in which the explicitly resolved top coat
microstructural features are embedded in a larger domain.
Within the computational cell, splat interfaces are modeled
as being located on a sinusoidal interface in combination
with a random distribution of pores. Parametric studies are
conducted for different splat interface waviness, spacing,
pore volume fraction and fracture properties of the splat
interface. The results are quantified in terms of crack
nucleation temperature and total microcrack length. It is
found that the amount of cracking in TBCs actually
decreases with increased porosity up to a critical volume
fraction. In contrast, the presence of splats is always
detrimental to the TBC performance. This detrimental
effect is reduced for the splat interfaces with high waviness
and spacing compared to those with low waviness and
spacing. The crack initiation temperature was found to be
linearly dependent on the normal fracture properties of the
splat interface. Insights derived from the numerical results
aid in engineering the microstructure of practical TBC
systems for improved resistance against thermal fracture.
Keywords cohesive elements � fracture � porosity � splats �thermal barrier coatings
Introduction
Thermal barrier coatings (TBC) are heat insulation layers
applied on the high-temperature regions of aircraft jet
engines in order to protect the crucial structural compo-
nents against overheating and consequently to extend the
lifetime of these components. They also improve the
combustion efficiency of the engine by allowing higher
operational temperature. The most common TBC system is
a multilayered system. It consists of two layers; an outer
ceramic layer that protects the substrate from high-tem-
perature gases and an intermediate metallic layer which
provides adhesion between the substrate and the ceramic
layer. The metallic layer also protects the substrate from
high-temperature oxidation and corrosion. The outer cera-
mic layer is called top coat (TC) and is often made of yttria
stabilized zirconia (YSZ). The metallic layer is called bond
coat (BC) and is usually made of MCrAlY (M refers to Ni
or Al or a mixture of these two. The coating system is
subjected to a thermal cycle during operation where the
temperature ranges from ambient to its operating value
(around 1200 �C). During operation, a thin thermally grownoxide (TGO) layer consisting of alumina (Al2O3) is formed
at the TC/BC interface due to oxidation of the bond coat.
During each thermal cycle, thermal stresses are generated
in the coating due to a mismatch in coefficients of thermal
& Jayaprakash [email protected]
Sathiskumar A. Ponnusami
Sergio Turteltaub
Sybrand van der Zwaag
1 Faculty of Aerospace Engineering, Delft University of
Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands
2 Department of Mechanical Engineering and Aeronautics,
City, University of London, Northampton Square,
London EC1V 0HB, UK
123
J Therm Spray Tech
https://doi.org/10.1007/s11666-019-00949-y
http://crossmark.crossref.org/dialog/?doi=10.1007/s11666-019-00949-y&domain=pdfhttps://doi.org/10.1007/s11666-019-00949-y
expansion (CTE) of the TBC layers. These thermal stresses
along with the growth of the TGO layer lead to the
nucleation and evolution of microcracks in the coating as
illustrated in Fig. 1. With the increase in thermal cycles,
these microcracks coalesce to form a larger crack which
results in final failure of the coating known as spallation.
Conventional TBCs are predominantly manufactured
either by an electron beam physical vapor deposition (EB-
PVD) process or the air plasma spray (APS) technique (Ref
1). In the EB-PVD technique, the coatings are deposited on
the substrate in vacuum using a high-energy electron beam
(Ref 2). This technique produces a uniform coating with a
fine columnar grain structure. These coatings offer superior
strain tolerance, thermal shock and oxidation resistance
which ultimately leads to prolonged service life. In the
APS method, ceramic particles are melted and sprayed onto
the substrate at atmospheric pressure using plasma jet (Ref
3). APS TBCs have a shorter lifetime compared to EB-
PVD TBCs due to its layered microstructure and higher
number of defects. However, APS remains the preferred
manufacturing method in the fields of aerospace and power
generation gas turbines because of its low cost and high
production efficiency (Ref 4). A schematic diagram of the
microstructure of the APS TBC and its failure behavior is
presented in Fig. 1.
The distinctive microstructural features of APS TBCs
are splats in addition to other features such as pores,
microcracks and interface roughness. Splats are building
blocks of the APS TBCs which are formed during the
solidification process of the sprayed ceramic particles (Ref
5). The interfaces between the splats are usually weak. The
characteristics of the splat interfaces are determined by the
spraying parameters (Ref 6–8). Literature studies on TBC
microstructure show that the presence of splats along with
microstructural pores significantly influences the material
properties and failure behavior of the TBC (Ref 9–13).
Multiple efforts have also been undertaken in the liter-
ature to model and predict the influence of splat interfaces
on thermo-elastic properties of TBCs (Ref 14–17). In the
work (Ref 14), real microstructural images are used to
predict the effective thermal conductivity and stiffness
using finite element analysis. The stiffness reduction due to
splats is obtained indirectly by calculating the difference
between the stiffness values of finite element prediction of
as-sprayed (with splats) and experimental measurements of
thermal-cycled (no splats) samples, respectively. Similar
type of work is also carried out in (Ref 15) using image-
based extended finite element modeling. In addition, the
evolution of the stress intensity factor and the quenching
stress as a function of intra-splat cracks and substrate
temperature is also analyzed in their study. Thermal con-
ductivity of splat interfaces is obtained in (Ref 16) through
iterative finite element computations and by mapping the
calculated effective thermal conductivity with the experi-
mental measurements. A finite element model is generated
using real splat interface distribution obtained from frac-
ture image analysis. A finite element analysis on idealized
YSZ model system to analyze the effect of splat interfaces
on thermal conductivity of TBC is carried out in (Ref 17).
Literature studies to predict the influence of all aspects
of the TBC microstructure on its failure behavior are lim-
ited. Some studies are focussed only on the effect on TC/
(b)(a)
Spallation
micro-cracks
TopCoat (TC)
Bond Coat (BC)
Splat
Pores
Crack coalescence and TBC failure
Uneven deformationsdue to thermal cycling
Heating:expansion
Cooling:contraction
TBC
TGO
BC
TGO growth strain
TBC loading conditions
Thermally-Grown Oxide (TGO)
Fig. 1 A schematic APS TBCsystem showing the failure
mechanisms and the governing
loading conditions
J Therm Spray Tech
123
BC interface and microstructural pores (Ref 18, 19). A
recent numerical study has also included the presence of
splats, although authors have considered a single type of
microstructure (Ref 20). Experimental observations show
that the failure behavior of the TBC is significantly influ-
enced by the splats (Ref 11, 21, 22). For instance, in
addition to the microstructural pores, the stacking config-
uration and the bonding between the splats are also
important for the fracture resistance of coatings (Ref 21). It
is, therefore, the objective of this research to carry out a
systematic numerical study to investigate the effect of
interface topology and its fracture strength on the TBC
fracture behavior in the presence of microstructural pores.
Furthermore, concurrent multiscale modeling setup is
adopted to include the free edge effect which is relevant in
terms of interpreting experimental results of coated sam-
ples. The effect of splat interfaces is investigated using a
parametric TBC model with realistic pore distribution
corresponding to various splat interface features, namely
waviness, spacing and also the strength. The scope of this
research is relevant to the TBC community for
microstructure optimization to enable them to choose the
right set of processing and spraying parameters to get the
desired splat interface characteristics.
Multiscale Finite Element Model of TBCMicrostructure
Overall Geometry
The modeling of the TBC is carried out in a two-dimen-
sional domain under plane strain assumptions. A two-scale
concurrent multiscale modeling approach is adopted in
which the explicitly resolved TC microstructural features
are embedded in a much larger domain of the TBC with an
homogenized TC layer, as shown in Fig. 2. TBC
microstructural features such as pores, interface roughness
and splat interfaces are modeled explicitly in the TC layer
of the embedded computational cell as depicted in
Fig. 2(b).
The dimensions of the TBC geometry considered in this
work are derived from the disk-shaped APS TBC samples
developed within the research consortium (Ref 23) for
microstructure characterization and thermal cycling
behavior. The total thickness and the radius of the disk-
shaped sample are 6 mm and 15 mm, respectively. The
width of the embedded computational cell is considered as
480 lm (Ref 24). More details about the geometry and themodeling setup can be found in (Ref 18).
TBC computational cell is enriched with pore features
that are representative of TC porosity measurements
obtained as part of the collaborative work (Ref 23). For
conciseness, only the statistical distribution of the porosity
measurements is provided in Table 1. The pores are
modeled as an ellipsoidal quantity with an aspect ratio
(AR), orientation and size given in Table 1 for modeling
convenience. The pores are distributed randomly within the
TBC computational cell.
For simplicity, the interface waviness between TC and
BC and also the horizontal splat interfaces are represented
as a sinusoidal curve. The vertical coordinate yn of the n-th
splat interface is given by as a function of the horizontal
coordinates x as
ynðxÞ ¼ A0Cn cosðx 2p=kÞ þ nh ðEq 1Þ
where A0 and k corresponds to the reference amplitude andwavelength of the sinusoidal curve, respectively. The
subscript n refers to the types of interfaces in the TC layer
(n = 0 corresponds to the TC/BC interface and n [ 0
Top-Coat 500 μm
taoC-dnoB taoC-dnoBmμ002 mμ002
x
y
Substrate
Free
edg
e
6.0
mm
(a)
(b)
(c)
(d)
Fig. 2 A schematic ofconcurrent multiscale TBC
model with detailed
microstructure
J Therm Spray Tech
123
corresponds to the splat interfaces), h and C denote the
spacing between the two adjacent interface and interface
waviness, respectively. The waviness parameter C ranges
from C ¼ 0 (for a flat interface) to C ¼ 1 (for a sinusoidalinterface with amplitude A0. The wavelength (k) and initialamplitude (A0) of the interface are assumed to be constant
with a specified value of 60 lm and 10 lm, respectively(Ref 24). The vertical splat interfaces are modeled as
straight lines, and they are distributed randomly between
the horizontal splat interfaces as shown in Fig. 2(c). The
number of vertical splat interfaces between any two suc-
cessive horizontal interfaces is set to a value of 10 over the
length of the explicitly modeled domain.
Simulation Setup
The microstructure is meshed with three-noded plane strain
triangular elements (CPE3) using GMSH to model the bulk
response of the individual TBC layers. The fracture
behavior of the TBC is modeled using a cohesive zone
model which is implemented in the finite element frame-
work using the zero thickness four-noded cohesive element
(COH2D4). It is also important to mention that the fracture
process is modeled only in the computational cell and the
outer regions of the TBC only can respond as a homoge-
nized featureless elastic medium. Also, the elastic response
of the splat interfaces themselves are not considered in the
analysis since the interfaces are very thin compared to the
thickness of the splats. In other words, the constitutive
behavior of the splat interfaces is governed only by its
fracture properties, defined through zero thickness cohesive
element. To enable arbitrary crack initiation and propaga-
tion, the cohesive elements are inserted at every bulk ele-
ment interface of the TBC computational cell using a
MATLAB script (Ref 25). However, the cracks are allowed
to propagate only along inter-element boundaries which
lead to a mesh dependency effect. Hence, to obtain a
converged fracture pattern, a fine mesh size of 1 lm is usedin the computational cell region with a random mesh pat-
tern that mitigates mesh dependency and provides mean-
value convergence. The outer elastic regions of the TBC
are coarsely meshed with an average element size of 150
lm to reduce the computational time. The loading condi-tion considered in this work corresponds to a single thermal
cycle of as-deposited TBC system. A typical thermal cycle
of a TBC consists of three phases namely the heating,
dwell and cooling phase. In the heating and dwell phases of
the thermal cycle, the TBC is assumed to be stress free as
these coatings are deposited at high temperature. Hence,
only the cooling phase of the thermal cycle is considered in
the analysis, where the temperature is decreased from its
typical operating value of 1100 to 30 �C. Simulations arecarried out under uniform temperature distribution which
corresponds to the testing of samples in an oven (uniform
temperature). The case of non-uniform temperature distri-
butions has been studied experimentally in (Ref 26).
Stresses appear in the TBC system during cooling due to
the thermal contraction and the mismatch in coefficients of
thermal expansion as shown in Fig. 1. The cooling rate
does not play a role as the simulations are based on a quasi-
static analysis. The nonlinear fracture simulations are car-
ried out in the FEA package Abaqus using an implicit
Newton–Raphson solver.
Constitutive Models and Material Properties
The bulk response of the different layers of TBC is
assumed to be linearly elastic and isotropic. The fracture
behavior of the TBC is modeled using a bilinear cohesive
law (Ref 27) which is governed by the fracture strength and
fracture energy. Material parameters used for individual
TBC layers are summarized in Table 2. Elastic and ther-
mal properties of the TBC layers are considered to be the
same values used in the earlier work (Ref 18). The fracture
properties such as normal strength and toughness of the
TC, TGO and BC layers are in correspondence with the
values reported in (Ref 28–30). The mode I fracture
energies (GIC) given in Table 2 are calculated from the
toughness values (KIC) under plane strain assumption. The
ratio of shear strength to normal strength (c) for the TClayer, TGO layer and splat interfaces is assumed arbitrarily
to have a value of 4 to suppress the failure of TBC in
planes that are not parallel to the top surface in accordance
with experimental observations. The mode I fracture
Table 1 Modeling parametersfor random pore generation
Geometrical features Modeling parameters, %
Volume fraction 10
Micro-porosity (SP) 5 (size = 25 lm2)
Macro-porosity (LP) 5 (size = 75 lm2)
Round-shaped porosity 5 (AR = 1.5) [4 LP, 4 SP]
Lamellar-shaped porosity 5 (AR = 3)
Horizontally oriented lamellar porosity 2.5 (0�) [1.75 LP, 1.75 SP]Inclined lamellar porosity 2.5 (± 45�) [1.75 LP, 1.75 SP]
J Therm Spray Tech
123
energies GIC reported in Table 2 are calculated from the
fracture toughness values. For convenience, the same value
of c is also used to define the ratio between mode II andmode I fracture toughness.
The effective (reduced) elastic modulus of 80 GPa is
used for the outer (homogenized) TC layer. The fracture
properties of TC/BC interface are assumed to have the
same values as the BC layer. The cohesive stiffness
parameter is assigned with a sufficiently large value of 1010
GPa to eliminate the influence of artificial compliance
introduced through the cohesive law.
Results and Discussions
Parametric simulations are carried out to analyze the
influence of the TBC microstructure such as splat inter-
faces and pores on TBC failure behavior. In addition, the
effect of splat interface fracture properties is also consid-
ered in this study. The results are discussed in terms of
crack initiation temperature and total length of all micro-
cracks formed in the computational domain at the end of
the cooling cycle for each parametric case. The crack ini-
tiation temperature is defined based on a predefined initi-
ation length to avoid a mesh dependency effect. Predefined
initiation length is defined as the minimum total length of
consecutively failed cohesive elements required to form a
measurable microcrack. Based on the convergence analysis
carried out in (Ref 18, 24), a predefined length of 3 lm isused to define the crack initiation temperature for all the
parametric simulations. The failure of the cohesive element
is defined based on energy dissipation and the element is
considered to have failed when it dissipates 95% of its total
fracture energy. The TC layer is assumed to have com-
pletely failed if it becomes detached from the BC layer.
Effect of TBC Microstructural Features
In this section, the effect of individual microstructural
features on fracture behavior of the TBC is investigated.
Three different TBC models with explicitly represented
microstructures: (1) only pores, (2) only splat interfaces
and (3) combined splat interfaces and pores are considered
for this analysis along with the dense (defect free) TBC.
The pores are distributed randomly in the TC layer with
features given in Table 1. As discussed in the modeling
setup, the horizontal splat interfaces are modeled using
Eq 1 with the splat interface waviness and spacing of 0.8
and 12.5 lm, respectively. To include the effect of ran-domness of the pore distribution and vertical splat inter-
faces in the analysis, five different realizations are
considered. To illustrate the effect of splat interfaces in the
TBC failure process, stress distributions (ryy) along withthe crack pattern at the end of the thermal loading step for
two different microstructural configurations (namely TC
layer with pores and combined splat interfaces and pores)
are shown in Fig. 3. The overall stress distribution (ryy) isin correspondence with the studies carried out in the lit-
erature (Ref 19, 31). As observed in Fig. 3, the peaks and
valleys of the TC/BC interface lead to tensile and com-
pressive states of stress (ryy), respectively. The CTE mis-match between the layers and the presence of pores result
in a complex stress field especially at the vicinity of pores
as shown in Fig. 3. Also, for both configurations, the cracks
tend to nucleate and propagate from the edge due to tensile
stress (ryy) generated out of the free edge accompanied bylocal stress concentration near the pores. However, as
shown in Fig. 3(a), (b), the presence of splat interfaces has
a significant effect on the TBC cracking behavior both in
terms of crack nucleation and propagation. For the TBC
with combined splat interfaces and pores, the cracks
propagate mostly along the splat interfaces. In case of TBC
with only pores, the crack propagation is governed by the
direction of local stress concentration generated by the
pores. It can also be observed that the effect of the cracking
remains relatively local since the stress distribution in the
TC sufficiently far away from the cracked regions remains
identical for both configurations.
The results are presented in terms of crack initiation
temperature and total crack length in Table 3 for the four
distinct TBC microstructural configurations as discussed.
It can be observed from Table 3 that the variations in
TBC microstructural configuration have a significant
influence on its failure behavior. For the microstructural
configurations without splat interfaces, the presence of
pores did not have a substantial effect on crack initiation
temperature compared to the dense case whereas a positive
influence of pores is observed for the configurations with
splat interfaces (i.e., a lower crack initiation temperature
Table 2 Elastic and fracturematerial parameters of the TBC
components
Layers E, GPa m a, 10�6 1/�C rn, MPa GIC, N/mm c
Top coat 200 0.15 12.5 200 0.01 4
Bond coat 130 0.3 14.5 500 0.3 1
Splat interface _ _ _ 75 0.002 4
TGO 380 0.15 6 380 0.06 4
Substrate 200 0.28 _ _ _ _
J Therm Spray Tech
123
compared to the splat interfaces only case indicates an
increased resistance against crack nucleation during cool-
ing). In terms of the total crack length, the presence of
pores has a positive effect for both the configurations (with
and without splat interfaces). However, this effect is more
pronounced for the microstructure without splat interfaces.
For instance, the total crack length of the dense TBC is
approximately two times higher than the TBC with pores.
This is due to the fact that the presence of pores increases
the TBC compliance which reduces the strain energy
contribution to the crack driving force (Ref 32). The pos-
itive influence of the pores on TBC lifetime is reported in
the literature through experimental measurements (Ref
33, 34). On the other hand, a TC with splat interfaces leads
to early crack initiation and also to a larger crack length,
which is expected because of the weak interface. From
Table 3, it can be concluded that the presence of pores
results in an improved resistance of the TBC against
fracture whereas the presence of splat interfaces is detri-
mental to the TBC. To understand the effect of splat
interfaces on TBC failure behavior, parametric simulations
are carried out in the next section for different geometries
and fracture properties of the splat interfaces.
Parametric Simulation
The parametric studies are carried out for three different
parameters such as splat interface waviness, spacing and
porosity, and the variations are listed in Table 4. The
simulation results are discussed in terms of crack initiation
temperature and total crack length. Similar to the study on
effect of TBC microstructural features, five different real-
izations are utilized for each parametric case to obtain the
−1000
−600
−200
0
200
400MPa
σyy
−400
−800
(a) Pores (b) Pores and splats
Fig. 3 Stress distribution (ryy) and failure behavior of TBC at T = 30 �C for two distinct microstructural configurations. (a) Pores and(b) combined splats and pores
Table 3 Effect of TBC microstructural features
Microstructural features Crack initiation temperature, �C Total crack length at room temperature, mm
Dense (no defects) 330 0.16
Pores 310 ± 50 0.07 ± 0.01
Splat interfaces 800 ± 5 0.28 ± 0.03
Splat interfaces and pores 680 ± 16 0.22 ± 0.05
Table 4 Summary of splat interface and pore geometrical parameterused
Microstructural features Geometrical parameters
Splat interface waviness (C) 0, 0.4, 0.8, 1
Splat interface spacing (h) 6.25, 12.5, 25 (lm)
Porosity (Vf ) 0, 10, 15, 20 (%)
J Therm Spray Tech
123
statistical variation due to the random distribution of pores
and vertical splat interfaces.
Effect of Splat Interface Waviness
To investigate the effect of splat interface waviness, four
different waviness values 0, 0.4, 0.8 and 1 are analyzed.
The splat interface spacing and porosity are fixed with a
value of 12.5 lm and 10 %, respectively. The wavinessvalue of 0 results in flat interfaces in the computational
domain, whereas the waviness of 1 corresponds to the
cosine curve with specified amplitude of 10 lm for all thesplat interfaces (see Eq 1). For other waviness values, the
amplitude of the splats (cosine curve) is scaled linearly
with the increase in number of splat interfaces.
The results of the simulations are summarized in Fig. 4
to show the influence of splat waviness on initiation tem-
perature and total crack length. From Fig. 4(a), it can be
observed that the crack initiation temperature shows a
weak dependency on splat interface waviness. This is due
to the fact that the crack initiation is governed mostly by
the free edge stress which is maximum at a region away
from the TC/BC interface. In this region, the change in
splat interface amplitude for waviness values less than 1 is
minimal because, with increase in number of splat inter-
faces, there is a decrease in amplitude. For a waviness
value of 1, the amplitude of the splat interfaces remain
unaffected which results in a trend toward delay in crack
initiation as shown in Fig. 4(a).
In terms of total crack length, the splat interface wavi-
ness shows a significant influence especially for the
waviness of 0 and 1 as shown in Fig. 4(b). The crack length
for the TBC with flat splat interfaces (waviness = 0) is
sensitive to the distribution of pores. Two out of five
realizations show complete failure of the TC with major
cracking close to the TC/BC interface. Hence, the statis-
tical variation of total crack length for zero waviness is
considered as inconclusive. This behavior is due to the
presence of a flat interface which favors the linking and
propagation of microcracks. In addition, the formation of
microcracks is influenced by the distribution of different
pore features. Complete failure of the TC occurs if these
microcracks reach a critical total length. For the splat
interfaces with waviness of 0.4 and 0.8, the total crack
length remains almost the same and it decreases by a factor
of 2 for the waviness of 1. Thus, in general, it can be
concluded that an increase in splat interface waviness
improves the resistance against thermal fracture of the
TBC. These findings are in agreement with indentation
tests on APS TBC samples (Ref 21) that show that the
fracture resistance is indeed improved significantly for
TBCs with rough splat interfaces. Similarly, thermal
cycling studies (Ref 35, 36) on TBC also conclude that the
bond coat roughness has a significant effect on TBC life-
time with higher roughness leading to an increase in TBC
lifetime.
Effect of Splat Interface Spacing
Another parameter of interest is the splat interface spacing,
which is a direct measure of the splat thickness. In the
current TBC modeling setup, splat interface spacing affects
both the interface waviness and the number of weak
interfaces within the TC layer (refer Eq 1). Hence, the
variations in splat interface spacing may have a significant
effect on the TBC fracture characteristics. In order to study
this effect, four different splat interface spacing given by
6.25, 12.5, 25 and 50 lm are considered. The values forsplat interface waviness and volume fraction are kept
constant at 0.8 and 10 %, respectively. The results obtained
from the analysis are summarized in terms of crack initi-
ation temperature and total crack length and are shown in
Fig. 5. As observed in Fig. 5(a), the crack initiation tem-
perature remains almost constant for the range of splat
interface spacing considered. Nevertheless, for the refer-
ence configuration with only pores (no splats) given in
Table 3, the crack initiation temperature is significantly
lower than the initiation values reported in Fig. 5(a). In
terms of total crack length, the results indicate that the total
crack length decreases nonlinearly with the increase in
Initi
atio
n Te
mpe
ratu
re (
°C)
Splat waviness 0 0.2 0.4 0.6 0.8 1
300
500
700
900
0 0.2 0.4 0.6 0.8 1Splat waviness
0
0.05
0.1
0.15
0.2
0.25
Tota
l Cra
ck L
engt
h (m
m)
(b)(a)
Vf = 10 %h = 12.5 μm
Vf = 10 %h = 12.5 μm
(Based on non-fullycracked samples only)
Fig. 4 Variation of (a) crackinitiation temperature and (b)
total crack length for different
splat interface waviness of 0
(flat), 0.4, 0.8 and 1 with the
fixed splat interface spacing of
12.5 lm and volume fraction of10%. The total crack length for
zero waviness (flat interface) is
inconclusive since it does not
include two fully failed samples
out of five simulations
J Therm Spray Tech
123
splat interface spacing as shown in Fig. 5(b). For a spacing
of 6 lm, the final crack length is highly sensitive to thedistribution of pores with three realizations predicting
complete TC failure. This inconclusive behavior is gov-
erned by the stress distribution close to the TC/BC inter-
face and the local stress concentration generated by the
pores. The decrease in total crack length with the splat
interface spacing is attributed to the reduced number of
weak interfaces and the increase in splat interface
waviness.
Effect of Pore Volume Fraction
In this section, the volume fraction of the pores is varied
with a constant splat interface waviness of 0.8 and a
spacing value of 12.5 lm. Four different pore volumefractions given by Vf = 0, 10, 15 and 20 % are considered.
Two distinct microstructure configurations are considered
in order to illustrate the effect of splat interfaces on the
failure behavior of TBC along with porosity. One config-
uration is created with only pores, and one configuration is
formulated with combined splat interfaces and pores. The
crack initiation temperature and total crack length for both
configurations are reported in Fig. 6.
For all porosity values considered, the presence of splat
interfaces significantly influences the failure characteristics
of the TBC as observed in Fig. 6. The presence of splat
interfaces leads to early crack initiation when compared to
the TC layer with only pores as shown in Fig. 6(a). The
crack initiation temperature remains approximately con-
stant for the TC layer with only pores, whereas the crack
initiation temperature decreases nonlinearly with an
increase in porosity for the microstructure with combined
splat interfaces and pores. For the TC layer with combined
splat interfaces and pores, the crack initiation temperature
of 10% porosity decreases from 800 to 700 �C whencompared with the zero porosity case. Upon further
increase in porosity, the crack initiation temperature
remains almost constant up to Vf = 15% after which it
decreases to 550 �C for Vf = 20 %. In terms of total cracklength, it can be seen that for both cases (with and without
splat interfaces) the trend remains almost the same. The
presence of pores improves the fracture resistance of the
TC compared to the dense TBC (see Fig. 6b). This is due to
the decrease in strain energy contribution to the crack
driving force with porosity as explained in the section on
the effect of TBC microstructural features. The scatter in
total crack length values between individual simulations
for a nominally identical sets of input parameters is
attributed to the complex interaction of different pore
features and also its interaction with the splat interface.
Also, it is important to note that complete failure of TBC
occurs for a critical value of the porosity is Vf = 30% for
TC with pores and Vf = 20% for TC with combined splat
(b)(a)
10 20 30 40 50Splat spacing (μm)
0
0.1
0.2
0.3
Tota
l Cra
ck L
engt
h (m
m)
10 20 30 40 50300
500
700
900
Initi
atio
n Te
mpe
ratu
re (º
C)
Splat spacing (μm)
Vf = 10 %C = 0.8
Vf = 10 %C = 0.8
(Based on non-fully cracked samples only)
Fig. 5 Variation of (a) crackinitiation temperature and (b)
total crack length for different
splat interface spacing of 6.25,
12.5, 25 and 50 lm with thefixed splat interface waviness of
0 and volume fraction of 10%
0 10 15 20 25 30Porosity (%)
100
400
700
1000
Initi
atio
n Te
mpe
ratu
re (
°C)
5
Splats & PoresOnly Pores
0 5 10 15 20 25 30Porosity (%)
0
0.1
0.2
0.3
Tota
l Cra
ck L
engt
h (m
m)
TC F
ailu
re
TC F
ailu
re
C = 0.8h = 12.5 μm
Splats & Pores
Only Pores
Fig. 6 Variation of (a) crackinitiation temperature and (b)
total crack length for different
volume fractions of 0(dense),
10, 15, 20, 30% with the fixed
splat interface waviness of 0 and
splat interface spacing of 12.5
lm
J Therm Spray Tech
123
interface and pores. The optimal porosity value remains
constant at Vf = 15% for both microstructural
configurations.
Effect of Fracture Properties
As discussed earlier, the constitutive behavior of the splat
interface is governed by its fracture parameters. Hence, the
variation of these parameters significantly influences the
fracture behavior of the TBC system. To study this effect, a
parametric analysis is carried out for distinct material
properties, expressed as ratios of a reference benchmark
material with fracture strength rTC0 and fracture energyGTC0 , as follows:
rTC ¼ frTC0 ;
GTC ¼ fGTC0ðEq 2Þ
where f is the fracture ratio. Note that both properties are
varied using the same fracture ratio (f).
The parametric study is done with fixed splat interface
waviness of 0.8, splat interface spacing of 12.5 lm andporosity of 10 %. Two distinct normal (fn) and shear
fracture (fs) ratios are considered to analyze the influence
of normal and shear fracture properties of the splat inter-
faces. For each fracture ratio, the simulations were carried
out for five different values given by 0.5, 0.75, 1, 1.5 and 2.
While studying the influence of one fracture ratio, the other
fracture ratio is fixed at the value of 1. In other words, to
study the effect of splat interface normal fracture proper-
ties, the normal fracture ratio (fn) is varied with values
given by 0.5, 0.75, 1, 1.5 and 2 for a fixed shear ratio (fs) of
1 and vice versa.
Crack initiation temperature and total crack length for
both normal and shear fracture ratios are shown in Fig. 7.
From Fig. 7(a), it can be observed that the crack initiation
temperature decreases almost linearly with increase in
normal fracture ratio. For the variations in shear fracture
ratio (fs), the crack initiation temperature remains unaf-
fected as shown in Fig. 7(c). This is because the normal
fracture properties, being always less than the shear frac-
ture properties for the splat interface, are the most critical
values that control the crack initiation. In terms of crack
length, the results indicate that the variation of the total
crack length with the normal fracture ratio is not linear as
shown in Fig. 7(b). In particular, a drastic increase in
damage is observed in the TC layer when the normal
fracture ratio is decreased to a value of 1 [i.e., total crack
length increases abruptly by a factor of 2.5 when compared
to the fracture ratio (fn) of 1.5]. Similarly, the results shown
in Fig. 7(d) are parameter value sensitive particularly,
when the shear fracture ratio is decreased below a certain
critical value. For instance, the complete failure of the TBC
occurs when the shear fracture ratio is decreased below the
value of 1. The critical value for the complete TBC failure
is decided by the value of the fracture parameters for which
the crack coalescence is favoured.
Effect of TGO Thickness
The above reported simulations are carried out for the as-
sprayed TBC system under single thermal cycle. However,
during thermal cyclic operation, the oxidation of the bond
coat results in growth of an additional layer called the
thermally grown oxide layer (TGO). The growth of this
additional layer affects both the stress distribution and the
crack evolution pattern due to its strong CTE mismatch
with the adjacent layers. Complete failure of the TBC
occurs when the TGO thickness is in the range of 8 to 12
lm (Ref 37, 38). In this section, the influence of TGO onTBC fracture behavior is analyzed. Due to computational
constraints, this effect is studied parametrically for a single
cycle. This is based on the assumption that the TBC will
undergo cracking only after the TGO thickness is increased
to a specified value. Simulations are carried out for four
different TGO thicknesses values given by tTGO = 0, 3, 6
and 9 lm. The microstructural features of the TC layersuch as porosity, splat interface waviness and spacing are
kept constant with a value of 10%, 0.8 and 12.5 lm,respectively. The pores are distributed randomly in the TC
layer with pore characteristics specified in Table 1.
The normal stress distribution in the vertical direction
(ryy) and the crack pattern in the TBC are shown in Fig. 8for two different TGO thicknesses tTGO = 0 lm (left inset)and 9 lm (right inset). From Fig. 8, it can be observed thatthe presence of TGO significantly influences the stress
distribution and cracking pattern in the TBC. The TGO
thickness tTGO = 9 lm leads to complete delaminationfailure of the TBC with majority of cracking on the splat
interface close to the TC/TGO boundary, whereas for the
TBC without a TGO layer(tTGO = 0 lm) only limitedcracking is observed. This is due to the altered TBC stress
fields especially close to the TC/TGO interface. The stress
concentration in the TBC is governed by two distinct
parameters, one due to the presence of pores and the other
due to the CTE mismatch between the layers for both cases
(with and without TGO layer). However, for the TBC with
TGO layer, the stress concentration close to the interface is
amplified as shown in Fig. 8. This is attributed to the strong
CTE mismatch between the TGO and the other layers (TC
and BC) compared to the TBC without TGO layer. Fur-
thermore, the presence of TGO also influences the stress
concentration in the vicinity of pores close to the TC/TGO
interface. For instance, the vertical normal stress (ryy) atthe proximity of pores close to the TGO layer is largely
J Therm Spray Tech
123
tensile for TBC with TGO layer, whereas the stress fields
are mostly compressive for TBC without TGO layer. The
stress concentration close to the TC/TGO interface is fur-
ther amplified with the TGO thickness. This results in early
initiation and propagation of microcracks at the horizontal
splat interface close to the TGO layer. Complete failure of
the TBC occurs when these microcracks coalesce to form a
major delamination crack. It is also important to note that
the edge crack in the TC region is minimally influenced by
the TGO layer when compared to the cracking in the TC
region close to the TC/TGO interface. This is expected as
the stress distribution in the TC region sufficiently away
from the TC/TGO interface is less affected by the presence
of the TGO layer. The influence of the TGO thickness on
the TBC fracture performance is given in Fig. 9 in terms of
the total crack length. The total crack length is plotted as a
function of four considered TGO thicknesses. From Fig. 9,
it can be seen that the increase in TGO thickness decreases
the mechanical integrity of the TBC system. A TGO
thickness of 9 lm results in complete failure. This behavior
(b)(a)
(d)(c)
Normal fracture ratio
0
0.1
0.2
0.3
Tota
l Cra
ck L
engt
h (m
m)
fS = 1Vf = 10 %h = 12.5 μmC = 0.8
Initi
atio
n Te
mpe
ratu
re (º
C)
0.5 1 1.5 20.5 1 1.5 2Normal fracture ratio
300
500
700
900
fS = 1Vf = 10 %h = 12.5 μmC = 0.8
Initi
atio
n Te
mpe
ratu
re (º
C)
Shear fracture ratio
300
500
700
900
fN = 1Vf = 10 %h = 12.5 μmC = 0.8
Shear fracture ratio 0.5 1 1.5 2 0.5 1 1.5 2
0
0.2
0.4
0.6
Tota
l Cra
ck L
engt
h (m
m)
Com
plet
e TC
Fai
lure
fN = 1Vf = 10 %h = 12.5 μmC = 0.8
Fig. 7 Variation of (a) and(c) crack initiation temperature
and (b) and (d) total crack
length of TBC with random
representation of pores for
different splat interface normal
and shear strength values
−1200
−800
−400
0
400
800MPa
σyyttgo = 0 μm ttgo = 9 μm
Fig. 8 Stress distribution in TBC with random microstructural pores at T = 30 �C for TGO thickness of 0 and 9 lm
J Therm Spray Tech
123
is due to the increase in stress concentration with TGO
layer thickness as discussed above.
Conclusions
Thermal fracture behavior of the APS TBC with explicitly
modeled splat interface and pores is analyzed using a
cohesive elements based finite element method. The
influence of splat interface geometric characteristics (such
as the roughness of the planes in which the splat interfaces
are located and their spacing), porosity and splat interface
material parameter (fracture properties) on TBC fracture
behavior is studied through parametric simulations. The
results of the parametric studies are reported in terms of the
crack initiation temperature and total microcrack length in
the computational domain upon cooling down from the
peak temperature of 1100 �C to room temperature (30 �C),whereby both the splat interface and pores are found to
exhibit a significant influence on the fracture behavior. The
following conclusions are drawn from the parametric finite
element investigations.
1. Microstructural features of the TBCs play a significant
role in determining its failure characteristics. With
reference to the fully dense TBC system, the presence
of pores improves the fracture resistance whereas the
presence of splat interface leads to early and more
extensive failure of the TBC.
2. The influence of splat interface waviness on the crack
initiation temperature is limited. The crack length for
the flat splat interface is sensitive to the distribution of
pores. In general, the increase in splat interface
waviness improves the TBC fracture resistance.
3. Splat interface spacing did not have a significant
influence on the initiation temperature, whereas the
total crack length decreases with an increase in splat
interface spacing.
4. The presence of pores improves the resistance against
TBC fracture for both microstructural configurations
considered. However, porosity beyond a critical value
leads to early failure.
5. On the effect of splat interface fracture properties, the
crack initiation temperature scales more or less linearly
with normal tensile strength of the splat interfaces. In
terms of crack length, the results are sensitive when the
fracture ratio values are reduced to a value below a
critical level. Complete failure of TBC occurs when
shear fracture ratio is decreased below a value of 1.
6. The increase in TGO thickness proportionally
decreases the mechanical integrity of the TBC system.
The results and insights as reported here aim to clarify
understanding the effect of TBC microstructure especially
splat interfaces and pores on failure behavior, which in turn
can aid in optimizing the processing and spraying param-
eters for improved performance/lifetime. Based on the
current simulations, TBC systems with an optimal porosity
value, having the splat interfaces arranged in non-planar
configuration, having a large splat interface spacing and a
high splat interface tensile strength perpendicular to the
splat interface plane, should give the best thermal cracking
resistance.
Acknowledgments This work was funded in part by the EuropeanUnion’s seventh framework program (FP7) through the NMP
SAMBA project (Grant Number 309849). We extend our sincere
thanks to our collaborator and SAMBA program leader Prof. W.G.
Sloof for his valuable support and interactive discussions. We also
acknowledge the use of a Matlab code to generate splat interfaces
microstructures as developed in a companion project (Ref 39).
Open Access This article is distributed under the terms of theCreative Commons Attribution 4.0 International License (http://crea
tivecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided you give
appropriate credit to the original author(s) and the source, provide a
link to the Creative Commons license, and indicate if changes were
made.
References
1. A. Feuerstein, J. Knapp, T. Taylor, A. Ashary, A. Bolcavage, and
N. Hitchman, Technical and Economical Aspects of Current
Thermal Barrier Coating Systems for Gas Turbine Engines by
Thermal Spray and EBPVD: A Review, J. Therm. Spray Tech-
nol., 2008, 17(2), p 199-2132. S. Gong and Q. Wu, Processing, Microstructures and Properties
of Thermal Barrier Coatings by Electron Beam Physical Vapor
Deposition (EB-PVD), Woodhead Publishing, In Therm. Barrier
Coatings, 2011, p 115-131
3. J.L. Xu and K.A. Khor, Plasma Spraying for Thermal Barrier
Coatings: Processes and Applications, in Thermal Barrier Coat-
ing. (Woodhead Publishing, 2011), pp. 99–114
4. A. Abdul-Aziz, Durability Modeling Review of Thermal- and
Environmental-Barrier-Coated Fiber-Reinforced Ceramic Matrix
Composites Part I, Materials, 2018, 11(7), p 1251-1267
TGO thickness (μm)
0
0.2
0.4
0.6To
tal C
rack
Len
gth
(mm
)
0 3 6 9
Vf = 10 %
C = 0.8h = 12.5 μm
TC F
ailu
re
Fig. 9 Variation of total crack length for different TGO thickness 0,3, 6 and 9 lm
J Therm Spray Tech
123
http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/
5. D.E. Wroblewski, R. Khare, and M. Gevelber, Solidification
Modeling of Plasma Sprayed TBC: Analysis of Remelt and
Multiple Length Scales of Rough Substrates, J. Therm. Spray
Technol., 2002, 11(2), p 266-2756. G.R. Li, G.J. Yang, C.X. Li, and C.J. Li, Sintering Characteristics
of Plasma-Sprayed TBCs: Experimental Analysis and an Overall
Modelling, Ceram. Int., 2018, 44(3), p 2982-29907. C. Lamuta, G. Di Girolamo, and L. Pagnotta, Microstructural,
Mechanical and Tribological Properties of Nanostructured YSZ
Coatings Produced with Different APS Process Parameters,
Ceram. Int., 2015, 41(7), p 8904-89148. E. Lugscheider and R. Nickel, Finite Element Simulation of a
Coating Formation on a Turbine Blade During Plasma Spraying,
Surf. Coatings Technol., 2003, 174, p 475-4819. M. Mutter, G. Mauer, R. Mücke, O. Guillon, and R. Vaßen,
Correlation of Splat Morphologies with Porosity and Residual
Stress in Plasma-Sprayed YSZ Coatings, Surf. Coatings Technol.,
2017, 318, p 157-16910. Z. Wang, A. Kulkarni, S. Deshpande, T. Nakamura, and H.
Herman, Effects of Pores and Interfaces on Effective Properties
of Plasma Sprayed Zirconia Coatings, Acta Mater., 2003, 51(18),p 5319-5334
11. J. Malzbender and R.W. Steinbrech, Fracture Resistance of
Atmospheric Plasma Sprayed Thermal Barrier Coatings, Surf.
Coatings Technol., 2012, 209, p 97-10212. T. Wakui, J. Malzbender, and R.W. Steinbrech, Strain Analysis
of Plasma Sprayed Thermal Barrier Coatings Under Mechanical
Stress, J. Therm. Spray Technol., 2004, 13(3), p 390-39513. G.R. Li, G.J. Yang, X.F. Chen, C.X. Li, and C.J. Li, Strain/
Sintering Co-induced Multiscale Structural Changes in Plasma-
Sprayed Thermal Barrier Coatings, Ceram. Int., 2018, 44(12),p 14408-14416
14. A. Kulkarni, Z. Wang, T. Nakamura, S. Sampath, A. Goland, H.
Herman, J. Allen, J. Ilavsky, G. Long, J. Frahm, and R.W.
Steinbrech, Comprehensive Microstructural Characterization and
Predictive Property Modeling of Plasma-Sprayed Zirconia
Coatings, Acta Mater., 2003, 51(9), p 2457-247515. P. Michlik and C. Berndt, Image-Based Extended Finite Element
Modeling of Thermal Barrier Coatings, Surf. Coatings Technol.,
2006, 201(6), p 2369-238016. L. Lu, F.C. Wang, Z. Ma, and Q.B. Fan, Anisotropic Effect of
Splat Interface on Thermal Conductivity of Plasma Sprayed YSZ
Coating, Surf. Coatings Technol., 2013, 235, p 596-60217. X. Guo, W. Zhao, Y. Zeng, C. Lin, and J. Zhang, Effects of Splat
Interfaces, Monoclinic Phase and Grain Boundaries on the
Thermal Conductivity of Plasma Sprayed Yttria-Stabilized Zir-
conia Coatings, Coatings, 2019, 9(1), p 2618. J. Krishnasamy, S.A. Ponnusami, S. Turteltaub, and S. van der
Zwaag, Computational Investigation of Porosity Effects on
Fracture Behavior of Thermal Barrier Coatings, Ceram. Int.,
2019, 45(16), p 20518-2052719. M. Białas, Finite Element Analysis of Stress Distribution in
Thermal Barrier Coatings, Surf. Coatings Technol., 2008,
202(24), p 6002-601020. Z.Y. Wei and H.N. Cai, Stress States and Crack Behavior in
Plasma Sprayed TBCs Based on a Novel Lamellar Structure
Model with Real Interface Morphology, Ceram. Int., 2019,
45(14), p 16948-1696221. J. Huang, W. Wang, X. Lu, S. Liu, and C. Li, Influence of
Lamellar Interface Morphology on Cracking Resistance of
Plasma-Sprayed YSZ Coatings, Coatings, 2018, 8(5), p 18722. C. Li, X. Zhang, Y. Chen, J. Carr, S. Jacques, J. Behnsen, M. di
Michiel, P. Xiao, and R. Cernik, Understanding the Residual
Stress Distribution Through the Thickness of Atmosphere Plasma
Sprayed (APS) Thermal Barrier Coatings (TBCs) by High Energy
Synchrotron XRD; Digital Image Correlation (DIC) and Image
Based Modelling, Acta Mater., 2017, 132, p 1-1223. W.G. Sloof. Self-Healing Thermal Barrier Coatings for Pro-
longed Lifetime (Funded by EU-FP7, Grant Number 309849)
24. J. Krishnasamy, S.A. Ponnusami, S. Turteltaub, and S. van der
Zwaag, Modelling the Fracture Behaviour of Thermal Barrier
Coatings Containing Healing Particles, Mater. Des., 2018, 157,p 75-86
25. S.A. Ponnusami, S. Turteltaub, and S. van der Zwaag, Cohesive-
Zone Modelling of Crack Nucleation and Propagation in Partic-
ulate Composites, Eng. Fract. Mech., 2015, 149, p 170-19026. Y. Wu, P. Hsu, Y. Wang, M.H. McCay, D.E. Croy, D. Moreno, L.
He, C. Wang, and H. Zhang, Laser Thermal Gradient Testing and
Fracture Mechanics Study of a Thermal Barrier Coating, J.
Therm. Spray Technol., 2019, 28(6), p 1239-125127. A. Hillerborg, M. Modéer, and P.E. Petersson, Analysis of Crack
Formation and Crack Growth in Concrete by Means of Fracture
Mechanics and Finite Elements, Cem. Concr. Res., 1976, 6(6),p 773-781
28. S.R. Choi and N.P. Bansal, Mechanical Behavior of Zirconia/
Alumina Composites, Ceram. Int., 2005, 31(1), p 39-4629. M. Munro, Evaluated Material Properties for a Sintered Alpha-
Alumina, J. Am. Ceram. Soc., 2005, 80(8), p 1919-192830. T.S. Hille, S. Turteltaub, and A.S.J. Suiker, Oxide Growth and
Damage Evolution in Thermal Barrier Coatings, Eng. Fract.
Mech., 2011, 78(10), p 2139-215231. R. Vaßen, G. Kerkhoff, and D. Stöver, Development of a
Micromechanical Life Prediction Model for Plasma Sprayed
Thermal Barrier Coatings, Mater. Sci. Eng. A, 2001, 303(1–2),p 100-109
32. M. Karger, R. Vaßen, and D. Stöver, Atmospheric Plasma
Sprayed Thermal Barrier Coatings with High Segmentation
Crack Densities: Spraying Process, Microstructure and Thermal
Cycling Behavior, Surf. Coatings Technol., 2011, 206(1), p 16-2333. M. Ahrens, R. Vaßen, D. Stöver, and S. Lampenscherf, Sintering
and Creep Processes in Plasma-Sprayed Thermal Barrier Coat-
ings, J. Therm. Spray Technol., 2004, 13(3), p 432-44234. N. Curry, N. Markocsan, L. Östergren, X.-H. Li, and M. Dorf-
man, Evaluation of the Lifetime and Thermal Conductivity of
Dysprosia-Stabilized Thermal Barrier Coating Systems, J. Therm.
Spray Technol., 2011, 22(6), p 864-87235. W. Nowak, D. Naumenko, G. Mor, F. Mor, D.E. Mack, R. Vaßen,
L. Singheiser, and W.J. Quadakkers, Effect of Processing
Parameters on MCrAlY Bondcoat Roughness and Lifetime of
APS-TBC Systems, Surf. Coatings Technol., 2014, 260, p 82-8936. R. Eriksson, S. Sjöström, H. Brodin, S. Johansson, L. Östergren,
and X.-H. Li, TBC Bond Coat–Top Coat Interface Roughness:
Influence on Fatigue Life and Modelling Aspects, Surf. Coatings
Technol., 2013, 236, p 230-23837. H. Dong, G.J. Yang, C.X. Li, X.T. Luo, and C.J. Li, Effect of
TGO Thickness on Thermal Cyclic Lifetime and Failure Mode of
Plasma-Sprayed TBCs, J. Am. Ceram. Soc., 2014, 97(4), p 1226-1232
38. O. Trunova, T. Beck, R. Herzog, R.W. Steinbrech, and L. Sin-
gheiser, Damage Mechanisms and Lifetime Behavior of Plasma
Sprayed Thermal Barrier Coating Systems for Gas Turbines—
Part I: Experiments, Surf. Coatings Technol., 2008, 202(20),p 5027-5032
39. S. Murali, Micromechanical Modelling of Fracture Behaviour in
Self-Healing Thermal Barrier Coatings. Master’s Thesis,
TUDelft, The Netherlands, 2017.
Publisher’s Note Springer Nature remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.
J Therm Spray Tech
123
Numerical Investigation into the Effect of Splats and Pores on the Thermal Fracture of Air Plasma-Sprayed Thermal Barrier CoatingsAbstractIntroductionMultiscale Finite Element Model of TBC MicrostructureOverall GeometrySimulation SetupConstitutive Models and Material Properties
Results and DiscussionsEffect of TBC Microstructural FeaturesParametric SimulationEffect of Splat Interface WavinessEffect of Splat Interface SpacingEffect of Pore Volume Fraction
Effect of Fracture PropertiesEffect of TGO Thickness
ConclusionsAcknowledgmentsReferences